i used city water without a problem for germination. it will work for growing also but i recommend reverse osmosis since it's so much cheaper than distilled and virtually the same thing.
heres my trick to a very high germination success rate. make sure your seeds are healthy, no premature white ones, no flat or black ones. i wouldnt even use bag seeds. get seeds of a certain strain cause chances are it will be a lot better than a bag seed. plus it will probably be feminized. dont soak in water overnight. some ppl do this but i find it a waste of time. get a paper towel moist. not dripping wet but enough to saturate it with water. tap water or hard water will work fine. fold it so it fits in a zip lock baggie. place as many seeds as you want but keep them apart from each other so the roots dont get tangled. seal the baggie and place it in like an empty cereal box or old board game. put it in a dark room that has about a temp of 70-80 degrees F, not really too critical but stay within room temp. check on it in 2-3 days. as soon as you see a root poking out it's ok to plant. i've even broken a root on accident and the seedling actually still survived. try your best to plant it tap root facing down. they will be fine without the root facing down, but it seems like they grow better with the root facing down. otherwise it may sorta grow at a slant.
if anything, chlorine may help kill certain bacterias and shit on the seeds. i recommend against it for watering, but germinating with it is just fine. at least from my own experience.